
Das Dokument ist frei verfügbar 

 Nachweis  Kein Nachweis verfügbar 

Abstract: Linear timeperiodic systems arise whenever a nonlinear system is linearized about a periodic trajectory. Examples include anisotropic rotorbearing systems and parametrically excited systems. The structure of the solution to linear timeperiodic systems is known due to Floquet's Theorem. We use this information to derive a new norm which yields twosided bounds on the solution and in this norm vibrations of the solution are suppressed. The obtained results are a generalization for linear timeinvariant systems. Since Floquet's Theorem is nonconstructive the applicability of the aforementioned results suffers in general from an unknown Floquet normal form. Hence we discuss trigonometric splines and spectral methods that are both equipped with rigorous bounds on the solution. The methodology differs systematically for the two methods. While in the first method the solution is approximated by trigonometric splines and the upper bound depends on the approximation quality in the second method the linear timeperiodic system is approximated and its solution is represented as an infinite series. Depending on the smoothness of the timeperiodic system we formulate two upper bounds which incorporate the approximation error of the linear timeperiodic system and the truncation error of the series representation. Rigorous bounds on the solution are necessary whenever reliable results are needed and hence they can support the analysis and e.g. stability or robustness of the solution may be proven or falsified. The theoretical results are illustrated and compared to trigonometric spline bounds and spectral bounds by means of three examples that include an anisotropic rotorbearing system and a parametrically excited Cantilever beam. 


